A More Immortal Atlas

Does 1 + 1 = 2?  It may be useful to recall the thoughts of Socrates
on this subject, as recorded by Plato in Phaedo:

 "I will not even allow myself to say that where one is added 
  to one, either the one to which it is added or the one that is 
  added becomes two, or that the one added and the one to which 
  it is added become two because of the addition of the one to 
  the other.  I wonder that, when each of them is separate from 
  the other, each of them is one, but when they are come near to 
  one another, this is the cause of their becomming two, the 
  coming together.  Nor can I any longer be persuaded that when 
  one thing is divided, this division is the cause of its becoming 
  two, for just now the cause of becoming two was the opposite.  
  At that time it was their joining, and one was added to the 
  other, but now it is because they are separated from each other.

  I do not any longer persuade myself that I know why a unit or 
  anything else comes to be, or perishes or exists by the old 
  method of investigation, and I do not accept it, but I have 
  a confused method of my own.

  One day I heard someone reading, as he said, from a book of 
  Anaxagoras, and saying that it is Mind that directs and is 
  the cause of everything.  I was delighted with this cause 
  and it seemed to me good, in a way, that Mind should be the 
  cause of all.  I thought that if this were so, the directing 
  Mind would direct everything and arrange each thing in the 
  way that was best.  If then one wished to know the cause of 
  each thing, why it comes to be or perishes or exists, one had 
  to find what was the best way for it to be, or to be acted 
  upon, or to act.  On these premises then, it befitted a man 
  to investigate only, about this and other things, what is 
  best.  The same man must inevitably know what is worse, for 
  that is part of the same knowledge.

  As I reflected on this subject I was glad to think that I 
  had found in Anaxagoras a teacher about the cause of things 
  after my own heart, and that he would tell me, first, whether 
  the earth is flat or round, and then explain why it is so of 
  necessity, saying which is better, and that it was better to 
  be so.  If he said it was in the middle of the universe, he 
  would go on to show that it was better for it to be in the 
  middle, and if he showed me those things I should be prepared 
  never to desire any other kind of cause.

  I was ready to find out in the same way about the sun and 
  the moon and the other heavenly bodies, about their relative 
  speed, their turnings, and whatever else happened to them, 
  how it is best that each should act or be acted upon.  I 
  never thought that Anaxagoras, who said that those things 
  were directed by Mind, would bring in any other cause for 
  them than that it was best for them to be as they are.  Once 
  he had given the best for each as the cause for each, and 
  the general cause of all, I thought he would go on to explain 
  the common good for all, and I would not have exchanged my 
  hopes for a fortune.  I eagerly acquired his books and read 
  them as quickly as I could in order to know the best and the 
  worst as soon as possible.

  This wonderful hope was dashed as I went on reading, and saw 
  that the man made no use of Mind, nor gave it any responsibility 
  for the management of things, but mentioned as causes air and 
  ether and water and many other strange things... It is what the 
  majority appear to do, like people groping in the dark; they 
  call it a cause, thus giving it a name which does not belong 
  to it.  That is why one man surrounds the earth with a vortex 
  to make the heavens keep it in place, another makes the air 
  support it like a wide lid.  As for their capacity of being 
  in the best place they could possibly be put, this they do 
  not look for, nor do they believe it to have any divine force,
  but they believe that they will some time discover a stronger 
  and more immortal Atlas to hold everything together..."